Problem: Divide the following complex numbers: $\dfrac{9 e^{7\pi i / 6}}{3 e^{\pi i / 2}}$ (The dividend is plotted in blue and the divisor in plotted in green. Your current answer will be plotted orange.)
Answer: Dividing complex numbers in polar forms can be done by dividing the radii and subtracting the angles. The first number ( $9 e^{7\pi i / 6}$ ) has angle $\frac{7}{6}\pi$ and radius 9. The second number ( $3 e^{\pi i / 2}$ ) has angle $\frac{1}{2}\pi$ and radius 3. The radius of the result will be $\frac{9}{3}$ , which is 3. The angle of the result is $\frac{7}{6}\pi - \frac{1}{2}\pi = \frac{2}{3}\pi$ The radius of the result is $3$ and the angle of the result is $\frac{2}{3}\pi$.